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A Lewis acid acts as the "acceptor" while the Lewis base acts as the "donator" when forming a coordinate covalent bond. The thing that is being "accepted" or "donated" is electrons because even though this type of reaction has a specific name, we are still dealing with the valence shell of the molecule and/or atoms and the whole purpose of this is to create a coordinate covalent bond instead of a simple covalent bond. So, let's take for example the acid and base reaction between Boron Trifluoride and Fluorine. When looking at the Lewis structure of each one, you can see that in the structure for Boron Trifluoride, Boron needs one pair of electrons to form it's octet. Fluorine alone has seven electrons and is more than willing to form a coordinate covalent bond in order to form it's octet. In this acid and base reaction, the "acceptor" is Boron Trifluoride because this molecule is the one that is gaining the pair of electrons from the "donor", Fluorine. The reactions forms tetrafluoroborate anion (negative because the formal charge for Boron in this newly formed structure is -1).
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